Find the vertex, focus, and directrix of the parabola. Graph the equation.
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A)vertex: (-2, -2)focus: (-1.75, -2)directrix: x = -2.25
B)vertex: (2, 2)focus: (2.25, 2)directrix: x = 1.75
C)vertex: (-2, -2)focus: (-2, -1.75)directrix: y = -2.25
D)vertex: (2, 2)focus: (2, 2.25)directrix: y = 1.75

Question

Find the vertex, focus, and directrix of the parabola. Graph the equation.
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A)vertex: (-2, -2)focus: (-1.75, -2)directrix: x = -2.25 
B)vertex: (2, 2)focus: (2.25, 2)directrix: x = 1.75 
C)vertex: (-2, -2)focus: (-2, -1.75)directrix: y = -2.25 
D)vertex: (2, 2)focus: (2, 2.25)directrix: y = 1.75

Quizplus · Accepted Answer

The parabola opens to the left, which means the vertex is the point farthest to the right. Therefore, the vertex is (-2, -2). Since the parabola opens to the left, the focus is to the left of the vertex. This means that the focus is located at (-1.75, -2). The directrix is a vertical line that passes through the point that is the same distance from the vertex as the focus. Since the focus is to the left of the vertex, the directrix is a vertical line to the right of the vertex. This means that the directrix is the line x = -2.25. The graph of the parabola should look like a U-shape leaning to the left. The given equation is y = (x + 2)² - 2. This is in the standard form of a parabola with vertex (-2, -2). Since the parabola opens to the right and has a vertex to the left of the directrix, the directrix is a vertical line given by x = (x-coordinate of vertex) - (distance from focus to vertex), which is x = -2.25. The focus is to the right of the vertex and is at a distance of 0.25 units, so it is at (-1.75, -2).

Find the Vertex, Focus, and Directrix of the Parabola